Answer:
See explanation
Step-by-step explanation:
Function A is not clear; I will use the following in place of function A
Function A:
[tex]x \to\ 1 |\ 3 |\ 4 |\ 6[/tex]
[tex]y \to -1|\ 3|\ 5|\ 9[/tex]
Function B:
[tex]y = 2x + 4[/tex]
Required
Compare both functions
For linear functions, we often compare the slope and the y intercepts only.
Calculating the slope of function A, we have:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where:
[tex](x_1,y_1) = (1,-1)[/tex]
[tex](x_2,y_2) = (3,3)[/tex]
So, we have:
[tex]m = \frac{3 - -1}{3 - 1}[/tex]
[tex]m = \frac{4}{2}[/tex]
[tex]m = 2[/tex]
To calculate the y intercept, we set [tex]x = 0[/tex], then solve for y
i.e.[tex](x,y) = (0,y)[/tex]
Using the slope formula, we have:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where:
[tex]m = 2[/tex]
[tex](x_1,y_1) = (0,y)[/tex]
[tex](x_2,y_2) = (3,3)[/tex]
So, we have:
[tex]2 = \frac{3 - y}{3 - 0}[/tex]
[tex]2 = \frac{3 - y}{3}[/tex]
Multiply by 3
[tex]6 = 3 - y[/tex]
Collect like terms
[tex]y = 3 - 6[/tex]
[tex]y = -3[/tex]
So, for function A:
[tex]m = 2[/tex] -- slope
[tex]y = -3[/tex] --- y intercept
For function B
[tex]y = 2x + 4[/tex]
A linear function is represented as:
[tex]y = mx + b[/tex]
By comparison
[tex]m = 2[/tex] --- slope
[tex]b = 4[/tex] --- y intercept
By comparing the results of both functions, we have the following conclusion:
Functions A and B have the same slope (i.e. 2)
Function B has a greater y intercept (i.e. 4)
